Laying out the pins on the neck of the harp

In 2011, Michael Billinge wrote an interesting observation on the layout of the tuning pins on the neck of the Downhill harp. Talking about the way the tuning pins become more spread along the cheek band, as the angle of the neck becomes higher in the bass, he writes: “instead of an even change across the range, as might normally be expected, he seems to have done this in a series of blocks or groupings”

In his footnote, Billinge gives a list of the gaps between adjacent pins, and the way that they increase in steps. My chart below gives a visual representation of his data:

Pins spacing on the neck of the Downhill harp (mm) (data from Michael Billinge)

What made me think of this was that I was doing the same work this week on the Carolan harp. I tagged points on the laser-scan corresponding to the cheek-band holes in the left side (string side) cheek band, and then calculated the distance between each one. Plotting a graph of these distances showed clear groups of similarly-sized spaces.

Tuning pin spacing on the neck of the Carolan harp (mm)

Billinge does not say what the error margin on his measurements are, and so it is difficult to analyse them further. On the Carolan harp, the error on the picked points is less than 0.1mm, but the selection of what points to pick is much less accurate than that, since the scan is quite messy around the tuning pin, with lots of scanning artefacts. I would estimate the accuracy of my measurements as perhaps ±1mm

You can see on my graph that there is a certain amount of zig-zagging, alternating around an average value. I saw this also on the spacing of the string shoes on the belly, but I explained that as an artefact of the alternating shoe design. I’m less sure how to understand this alternating spacing on the neck.I have not done such a detailed measurement of any of the other harps, but the point positions of the tuning pins as used to generate the string charts for the Kildare and the Mullaghmast harps can be used to analyse the pin spacing. The accuracy here is perhaps more like ±3mm. The Kildare seems to show some evidence of grouping, but the Mullaghmast pins are clearly spaced incrementally, with each pin a little further from its neighbour than the previous one.

Pin spacing on the neck of the Kildare harp (mm)

Pin spacing on the neck of the Mullaghmast harp (mm) (cropped, the largest spacing is 116mm)

We could follow Billinge by averaging each group on the Carolan harp, and calculating a standard deviation from the average:

Pins 1-3: 17±1.5mm
Pins 3-6: 14.5±6mm (too erratically placed to say much)
Pins 6-12: 13±1.5mm
Pins 12-19: 14.5±1.5mm
Pins 19-26: 18.5±1.5mm
Pins 26-30: 22±1mm
Pins 30-32: 26±1mm
Pin 32-33 crosses the opened neck-pillar joint.
Pins 33-36: 28.5±1mm

I think this kind of analysis can give us ideas about the working methods of the old harp makers. We can imagine the makers of the Downhill and the Carolan harp, working with dividers to lay out groups of pinholes on the metal cheek-band, as well as using dividers to lay out the string-shoes equally spaced on the soundboard.

What then of the Mullaghmast harp, with its progressive spacing? A different school of harpmaking?

My header photo shows a rendering from the laser-scan, showing two points picked for holes 9, 8, 7, 6, 5, and 4. The position of each hole was calculated as an average of the positions of the two points. The background grid is 1mm x 10mm. The messy damage around hole 3 and the break in the neck is visible in the top-right corner.

5 thoughts on “Laying out the pins on the neck of the harp”

  1. I did the same work on the laser-scan of the Hollybrook harp, picking two points for each pin and averaging them to get a position for each pin, and calculating the distance between adjacent pins. My chart shows each distance with 1mm error bars; the point numbered “1” represents the distance from pin 1 to pin 2 on the string side of the neck, etc.

    Chart of Hollybrook harp pin spacing

    I think my chart shows that the Hollybrook may be laid out in this “groups” system. We could squint at the chart and imagine pins 1-19 with a spacing of about 13mm; pins 20-26 spaced about 15mm; 27-33 spaced about 22mm, and the lowest bass strings about 26mm.

    Pin 35 is on the neck-pillar joint. However the cheekband does not seem damaged at this point.

    The last pin is 37, and then there are two iron rivets through the neck which I have labelled 38 and 39. We can see that the first iron rivet is spaced at about 25mm from the last pin, which fits it nicely into this group, and implies that it may well (as I suspected) be a blocked pin hole 38. However the second iron rivet is spaced only 21mm further on, which is significantly less that this group of pin spacings, implying that it may not be a blocked pin hole.

    1. I think we need to be very cautious before using this work to draw any conclusion. I experimented with generating measurements from Karen Loomis’s scan rendering, plotting pixels in an image editing programme, and also estimating the uncertainty in the position of each pin. This chart shows the plotted positions from the rendering, with the error bars for each data point calculated as the uncertainty, combined in quadrature, of each of the two pin positions that the data point refers to.

      Hollybrook pin spacing from scan render

      I think this method has the potential to be a lot more accurate than point picking directly on the scan, though there are clear methodological traps. We have to take care to orient the scan properly, and probably it would be sensible to slice away the pin projections to give a clearer view of the cheekband holes. We also need to be very careful of scanning artefacts.

      I think the potential accuracy using this method is much better; I estimated pixel uncertainty on the data points and the clearest came out as +/- 0.5mm.

      For this new Hollybrook chart I am thinking that this could equally demonstrate a progressive, continuous increase in string spacing, or a stepped layout with four groups.

      I think that what this shows is that the maker’s tolerances when laying out the harp and drilling the holes starts to take over from the measurement accuracy (which is a good thing from a metrology point of view). I think that we have to be very careful when moving from this measured data to making a statement about the maker’s intention or the design principles.

      I think that the most important here is our handling of the measurement uncertainty, and our analysis of the uncertainty in a rigourous and scientific way, generating sensible estimates of error (uncertainty) and manipulating that data correctly. It is possible that some kind of Bayesian analysis of this data could help us to make more confident statements about the original design principles. It would also be very useful to get some figures for the typical tolerances for this kind of hand work, to be able to quantify the expected variance in the measured results. In the mean time, I recommend taking all the statements and conclusions presented by me on this blog post with a hearty dose of salt…

      Here’s my spreadsheet if you want to experiment with this method.

  2. I found Natalie Surina’s measurements of the Castle Otway harp, and I made a chart to show this data. These measurements were taken by hand from the harp, and I don’t know which side was being measured.

    Otway harp pin spacing

    It looks to me like there are just two groups here; pins 3 to 25 or 26 are spaced at about 17mm, and pins 26 to 36 are spaced at about 21mm.

    The neck is split across pin positions 1 and 2, which is why they have higher measured spacing.

  3. The three medieval harps form a distinctive group. All of them appear to have near enough evenly spaced pins.

    Here’s a chart showing Paul Dooley’s data for the Trinity College harp, extracted from his Sketchfab model which itself is based on his hand measurements as reported in his article: Paul Dooley, ‘Reconstructing the medieval Irish harp’, Galpin Society Journal LXVII, 2014.

    Trinity College harp pin spacing (from Dooley model)

    The Trinity College harp shows an even spacing averaging at about 12mm. The last few at each end seem to be slightly wider at 13 to 14mm but this is pretty much within the error margin. The Trinity harp has the remains of holes for a 30th pin in its cut-down cheekbands, but I don’t have position measurements for these.

    Karen Loomis sent me the figures she had extracted from her CT scans for the Lamont and Queen Mary harp, as reported in her thesis: Organology of the Queen Mary and Lamont harps, PhD thesis, University of Edinburgh, 2017. Here is the Lamont harp:

    Lamont harp pin spacing (Karen Loomis data)

    The Lamont harp shows an even pin spacing, averaging at 12mm. Note that the 32nd pin is not original but is added below the brass cheek band.

    Here is the Queen Mary harp:

    Queen Mary harp pin spacing (Karen Loomis data)

    The Queen Mary harp shows an even pin spacing, averaging at just over 11mm. The lowest 2 pins seem wider spaced, around 13mm, but pin 30 is the later addition beneath the brass cheek band so we should probably ignore it.

  4. Here is the Malahide 1 harp or Kearney 1 harp, which I inspected and photographed back in 2015:

    Malahide 1 / Kearney 1 harp pin spacing

    These measurements are taken from a photograph, scaled to the length of the longest string position, which is all a bit approximate and so I have made the error bars 3mm to indicate the reduced precision of the measurements. The photograph scaling may also be off, so the absolute numbers are not reliable here, but the proportions are right.

    This harp seems to have a similar spacing layout to the Mulagh mast harp, with a gradual and incremental increase in spacing towards the bass. (Though the Mulagh mast harp has a kind of exponential growth in the spacing as well as a “turn down” at the very bass, whereas this one has a more linear growth.)

    This harp has iron treble pins and brass bass pins, swapping between pins 21 and 22, but we can see that the pin spacing has already started increasing by the time we get to pin 21. If we think 21 and 22 may be the two na comhluighe g strings, then the transition from equal to increasing spacing is about one octave above that.

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